In the coordinate plane, a triangle has vertices at points $A(1, 2)$, $B(5, 6)$, and $C(1, 6)$. Determine the area of this triangle.

Use the formula for the area of a triangle given by the vertices $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$:

$$ ext{Area} = rac{1}{2} | x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) | $$